Well, I have a little experience with both. I live in Taipei, but have friends and family in Jungli.
If you do not want a car or scooter, I would suggest Taipei. You won’t match the convenience anywhere else in Taiwan. Jungli does have a couple of bus services. They look very old and scary, but will get you anywhere they want to go. That could range from a bus every ten minutes to a bus several times a day.
The only problem I have had with police/bureaucracy in Taoyuan county was having my ID checked by a bored policeman one time. Closer to Taipei, there seems to be a little more hassle in that regard (not much for me, though).
I would agree with others who have said that, if you do not live near the station, you will have a very “small town/world” life in Jungli. Taipei is more convenient, but you pay for it. If you are interested in being around westerners, go to Taipei. If you don’t care (like me), both are ok. It’s up to what you want.