They both have their pluses and neither is inherently "superior". The Garmin has more map options than the TomTom, even allowing the use of CityExplorer maps with improved pedestrian options and including mass transit for routes. If you plan to travel to specific foreign cities on vacation or business, the City Explorer maps can save you a lot of money over continent wide maps. The 1350T also includes free lifetime traffic and potentially less expensive map updates. The 1350 also offers "Ecoroute", a routing option that supposedly helps saves gas, and FM broadcast for sending navigation instructions over your car radio. The 340 doesn't offer any of this.
On the 340, it's hard to argue that you'll get more efficient routing in larger metro areas as much as 40% of the time (according to TomTom), Their IQRouting seriously improved route selections over their previous devices. Garmin also has no Mapshare equivalent which can be a handy way to make minor changes to your existing map. Particularly beneficial if you live in an area with frequent road closures or long-term construction. Mapshare gives you the ability to block the use of some of those roads for routing. If tinkering with menu options is important, the edge there to TomTom too. On the negative side, if you want traffic on your 340 it will cost you. Otherwise the two devices both offer lane assistance, TTS, and widescreens. You'll just have to compare the two feature sets and see which matches your specific needs/wants better.