Pokemon GO: Does higher player levels mean higher catch rates
This has been discussed in the subreddit /r/TheSilphRoad which is quite truthworthy, since a lot of discoveries about Pokemon Go data have been discovered there.
As pointed out in this post Analysis on Catch Rates and Encounters, the catch rate of an encountered Pokemon is determined by two factors :
The Base Capture Rate1 of the Pokemon, which only depend on the kind of Pokemon itself.
The Pokemon level, which depends only on your trainer level.
As you can see in this array1, the combination of those two elements gives us the final catch rate2. We notice that the higher the Pokemon level is, the lower the final catch rate is.
Since the Pokemon's level increases as fast as the trainer's level, a higher lever trainer will encounter Pokemon with lower Capture Rates.
What's more (thanks @Kat for pointing out), the combination of the Base Capture Rate and the Pokemon's level being the only thing that defines a Pokemon's catch rate, two trainers encountering the same kind of Pokemon with the same Pokemon will have the same catch rate, no matter what the levels of the two trainers are.
1 Those links are extracted from the previously mentionned post Analysis on Catch Rates and Encounters
2 Note that we don't have informations on how the kind of Pokeball influences the catch rate, but it does not really matter as we can obviously assume that a rarer Pokeball is giving a better catch rate independently from of the Trainer's level.