Food for thought
From personal experience - whilst the two are not mutually exclusive trying to do both at the same time will lead to a comprimise on both fronts.
People new to training always have a honeymoon period and can experience sizable change but unfortunately things slow down with time.
Pro Bodybuilders have off seasons where their sole goal is to get bigger, then when it comes to competition will trim down and change their training (lighter, more reps). They don't try and do both at once(not all anyway)
There are varying extremes of how they go about it. Some might only put on an extra 10-20lbs in the off season, but others balloon by 50lbs or more.
The added weight and support around the joints reduces injuries when lifting progressively heavier weights.
This is not meant to be a downer and is more relevant if you are trying to pack on some size(trying to get leaner will restrict your bodies nutrients supply). Don't be afraid of adding some extra bodyweight, you just have to make sure it doesn't run away with you.
Obviously if you are changing diet completely from a high fat one, then I'm sure you are going to see some good change on both fronts.
The moral and point I am getting at is to understand your long term goals and then workout the best way forward. If you are trying to pack on size, then the winter months are a good off season and you can be more relaxed on diet(eat enough but not chicken and rice the whole time

) then come summer its an opportunity to trim down, change the diet slightly, and the training. It ends up being a bit of a 2 steps forward, one step back(strength may drop) but in the long term you will be able to build good quality mucsle. Focus on one at a time.
Sometimes I;m a bugger and get caught in a permenant off-season mode, but I really like my food.