[AT&T, Rogers HTC One X, Telstra One XL] pwnx:
Got some more logs form LogcatX. Phone rebooting using Nike+ and TuneIn for these:

01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: reader_thread: Received 69 bytes from 278
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: QMI_CCI_RX: cntl_flag - 04, txn_id - 0000, msg_id - 0026, msg_len - 003e
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: reader_thread: Received 69 bytes from 278
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: QMI_CCI_RX: cntl_flag - 04, txn_id - 0000, msg_id - 0026, msg_len - 003e
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: reader_thread: Received 49 bytes from 278
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: QMI_CCI_RX: cntl_flag - 04, txn_id - 0000, msg_id - 0026, msg_len - 002a
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: reader_thread: Received 631 bytes from 278
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: QMI_CCI_RX: cntl_flag - 04, txn_id - 0000, msg_id - 0025, msg_len - 0270
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: reader_thread: Received 220 bytes from 278
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: QMI_CCI_RX: cntl_flag - 04, txn_id - 0000, msg_id - 0024, msg_len - 00d5
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: reader_thread: Received 14 bytes from 278
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: QMI_CCI_RX: cntl_flag - 04, txn_id - 0000, msg_id - 002c, msg_len - 0007
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: reader_thread: Received 14 bytes from 278
01-23 18:40:42.252 1008 1604 D QMI_FW : QCCI: QMI_CCI_RX: cntl_flag - 04, txn_id - 0000, msg_id - 002c, msg_len - 0007
01-23 18:40:42.252 1008 1153 I BootReceiver: Copying /data/tombstones/tombstone_06 to DropBox (SYSTEM_TOMBSTONE)
01-23 18:40:42.292 237 16242 W SurfaceFlinger: binderDied: Restart boot animation due to the death of window manager!
01-23 18:40:42.302 250 13562 W AudioFlinger: power manager service died !!!
01-23 18:40:42.302 250 13562 W AudioFlinger: power manager service died !!!
01-23 18:40:42.302 250 13562 W AudioFlinger: power manager service died !!!
01-23 18:40:42.302 21947 27215 W Sensors : sensorservice died [0x402b71d0]
01-23 18:40:42.302 28660 10688 W Sensors : sensorservice died [0x403d4698]
01-23 18:40:42.302 2508 2521 D libc : pt_debug : pthread_create->start_routine=0x402d9509, tls=0x55528f00, arg=0x53393f98
01-23 18:40:42.302 1530 19055 W Sensors : sensorservice died [0x51452530]
01-23 18:40:42.302 250 13564 W Sensors : sensorservice died [0x4039bda0]
01-23 18:40:42.302 2508 2520 W Sensors : sensorservice died [0x532973c0]
01-23 18:40:42.302 27696 2441 W Sensors : sensorservice died [0x512cc310]
01-23 18:40:42.302 2661 2672 D libc : pt_debug : pthread_create->start_routine=0x402d9509, tls=0x54fa6f00, arg=0x512aaf38
01-23 18:40:42.302 2508 2941 D libc : pt_debug : __thread_entry->func=0x402d9509
01-23 18:40:42.302 2508 2941 D libc : , tls=0x55528f00, arg=0x53393f98
01-23 18:40:42.302 2508 2941 D libc : pt_debug : pthread_create->start_routine=0x402d9509, tls=0x55628f00, arg=0x53393fa8
01-23 18:40:42.302 2508 2942 D libc : pt_debug : __thread_entry->func=0x402d9509

01-23 18:44:08.954 3084 3437 D QMI_FW : QCCI: reader_thread: Received 14 bytes from 293
01-23 18:44:08.954 3084 3437 D QMI_FW : QCCI: QMI_CCI_RX: cntl_flag - 04, txn_id - 0000, msg_id - 002c, msg_len - 0007
01-23 18:44:08.974 1313 1313 I wpa_supplicant: wlan0: wpa_supplicant_scan enter
01-23 18:44:08.974 1313 1313 I wpa_supplicant: wlan0: wpa_supplicant_scan wpa_s->conf->ap_scan=1 , scan_req =0
01-23 18:44:08.974 1313 1313 I wpa_supplicant: wpa_supplicant_trigger_scan +
01-23 18:44:09.014 2948 3205 W AudioFlinger: power manager service died !!!
01-23 18:44:09.014 2948 3205 W AudioFlinger: power manager service died !!!
01-23 18:44:09.014 2948 3205 W AudioFlinger: power manager service died !!!
01-23 18:44:09.014 2948 3205 W AudioFlinger: power manager service died !!!
01-23 18:44:09.024 237 545 W SurfaceFlinger: binderDied: Restart boot animation due to the death of window manager!
01-23 18:44:09.024 3469 4074 W Sensors : sensorservice died [0x513a5070]
01-23 18:44:09.024 3375 3635 W Sensors : sensorservice died [0x512919c0]
01-23 18:44:09.024 6779 6821 W Sensors : sensorservice died [0x531f4258]
01-23 18:44:09.024 3813 3826 W Sensors : sensorservice died [0x4ff13b00]
01-23 18:44:09.024 5014 5025 W Sensors : sensorservice died [0x52d59f20]
01-23 18:44:09.074 237 396 D memalloc: ion: Freeing buffer base:0x40d3d000 size:188416 fd:70
01-23 18:44:09.074 237 396 D memalloc: ion: Unmapping buffer base:0x40d3d000 size:188416
01-23 18:44:09.074 237 396 D memalloc: ion: Freeing buffer base:0x400cf000 size:4096 fd:71
01-23 18:44:09.074 237 396 D memalloc: ion: Unmapping buffer base:0x400cf000 size:4096
01-23 18:44:09.074 237 396 D memalloc: ion: Freeing buffer base:0x4285e000 size:188416 fd:74
01-23 18:44:09.074 237 396 D memalloc: ion: Unmapping buffer base:0x4285e000 size:188416
01-23 18:44:09.074 237 396 D memalloc: io

This one is just with TuneIn running

01-23 19:26:16.528 11628 18585 D libc : pt_debug : __thread_entry->func=0x531f1c45
01-23 19:26:16.528 11628 18585 D libc : , tls=0x54617f00, arg=0x53480c90
01-23 19:26:16.528 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.528 11497 11509 D WifiStateMachine: WiFiDisplay: getWifidisplayApEnabled=false
01-23 19:26:16.528 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.528 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.528 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.538 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.538 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.538 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.538 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.538 237 396 D memalloc: ion: Freeing buffer base:0x40d3d000 size:188416 fd:73
01-23 19:26:16.538 237 396 D memalloc: ion: Unmapping buffer base:0x40d3d000 size:188416
01-23 19:26:16.538 237 396 D memalloc: ion: Freeing buffer base:0x40094000 size:4096 fd:75
01-23 19:26:16.538 237 396 D memalloc: ion: Unmapping buffer base:0x40094000 size:4096
01-23 19:26:16.538 237 396 D libc : pt_debug : pthread_create->start_routine=0x403f1509, tls=0x42f4df00, arg=0x4044bfc8
01-23 19:26:16.538 11628 11628 D PhoneStatusBar: disable: < expand icons alerts TICKER* system_info back home recent clock >
01-23 19:26:16.548 237 18586 D libc : pt_debug : __thread_entry->func=0x403f1509
01-23 19:26:16.548 237 18586 D libc : , tls=0x42f4df00, arg=0x4044bfc8
01-23 19:26:16.578 237 3065 D memalloc: ion: Allocated buffer base:0x45fb7000 size:3768320 fd:69
01-23 19:26:16.578 237 3065 D memalloc: ion: Allocated buffer base:0x40094000 size:4096 fd:71
01-23 19:26:16.588 11628 11628 D memalloc: ion: Mapped buffer base:0x56373000 size:3768320 offset:0 fd:85
01-23 19:26:16.588 11628 11628 D memalloc: ion: Mapped buffer base:0x5111e000 size:4096 offset:0 fd:87
01-23 19:26:16.859 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.869 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.869 11497 11976 D WifiStateMachine: WiFiDisplay: getWifidisplayApEnabled=false
01-23 19:26:16.869 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.869 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.869 11628 11628 E m0narX_tweaks: Error loading HEQS from theme: android.content.pm.PackageManager$NameNotFoundException: venom.systemui.theme.null
01-23 19:26:16.869 11628

Not sure how much these help considering they're cut off when it restarts.