Bitrate is an indicator of how much data is used in a given amount of time...basically, get 2 songs with a the same bitrate but one is twice as long, the longer one will be twice the size. Get 2 with the same length, but one with half the bitrate, and it will be half the size.
The more data is used, the higher quality the file. By converting from m4a 262 to MP3 320, you converted to a larger file.
Keep the m4a. Firstly, upconverting a bitrate is bad for quality - it is creating data that is not there. It is like doubling the resolution of a jpeg - it won't be as crisp. It's larger, but no higher quality. Also, converting between lossy formats isn't good either - each music format uses different psychacoustic models. These models determine what is removed - stuff that is supposedly less noticable to human hearing should it be missing. By converting an m4a to an mp3, you have applied both those psychoacoustic models, removing more of the data than just using one.
Upconverting bitrate, converting between lossy formats, or converting from lossy to lossless, are all degrading the song more than is necessary. The only truly "proper" (if they can be called that) audio conversions are within the same format to a lower bitrate (from the best source available - still not as high as a lossless or the source audio), or converting from lossy to lossless. Something along the lines of mp3 320 to mp3 128 or FLAC to mp3. Converting from m4a 262 to mp3 320 takes up more memory, for less quality. It is not a proper conversion, by any means, and I would recommend keeping the m4a files. Just because the file is 320 - does not mean the quality is. It's like upscaling from standard to HD - yeah, the 1080p resolution is there - but the quality is not.