Using and comparing different Nnavigation apps has beccome almost a hobby for me so I've had a lot of time to reflect on what's available. I've used pretty much every navigation app under the sun - at least on Android.
Assuming map data is up to date (no new bits of road, long term closed roads etc), Tomtom destroys Google for sensible rerouting around traffic - and accuracy of traffic info. The main difference, I think, is Tomtom's historic speed profile data that acts in conjunction with the live traffic. It has data for average speed for time of day and day of the week for every road (not just the main ones). The live traffic can also theoretically detect traffic on any road. I have seen it work occasionally even on side streets. This means that with Tomtom, diverting off a main road is not just a voyage into the unknown. If Google sends you on side streets or rural white roads, it may well be out of the frying pan into the fire (pretty much the same on the majority of other apps that offer traffic rediversion). Tomtom's traffic is not correct 100% but I'd say it's right more often than not. I've grown to trust it - I used Tomtom's own app for a year before switching to Route 66 and have seen it improve significantly as it's been upgraded.
The cheapest way to get Tomtom traffic in a navigation product is Route 66 Navigate on Android or iPhone. It has a 30 day trial, including Tomtom HD traffic. I've been using it about 7 months. In short - it's brilliant. It uses a slightly different routing algorithm from Tomtom but the same data. I keep checking Google maps to see if updates have changed it much but it's usually nowhere near as good as Tomtom for any routes that send you off the beaten track.
Both Route 66 and Tomtom can be set to either automatically reroute if faster routes are detected or to ask the user. I prefer the entirely automated option for entirely hands free operation.
The disadvantage of Route 66 and Tomtom is they're never close to Google for keeping maps up to date. Updates are quarterly on Tomtom and less often on Route 66. They both allow you to block part of the route to mitigate this though. Also, the search and POI info in Tomtom and Route 66 is nowhere near as google maps. There are occasions when I'll find the location in Google Maps and then use Route 66 to Navigate.
Tomtom's own app is also better than Google for traffic avoidance but it's more expensive than Navigate and pretty clunky (especially the Android version).