Is there a difference on how these two words should be used? I see 牛肉 used a lot more than ビーフ, but I'm wondering if there is a certain context for each of the two words.
牛肉 is used nearly universally, but use ビーフ on a case-by-case basis where you know the name of the food uses this instead (ビーフ is often favored in names of dishes).
The two words are interchangeable in meaning, but that doesn't go to say that they're interchangeable in speech. Both ビーフ and 牛肉 mean the same thing, but these are used differently.
For the most part, 牛肉 is the standard word for cow meat (i.e. beef). At shops, in cooking books and so on, this is more common in the general sense.
In a non-general sense, ビーフ very often appears in names of dishes or types of beef. For example
Beef is restricted in usage mostly to names of foods, but never used commonly to refer to cow meat in general, for which 牛肉 is standard.
While the meanings are practically identical, ビーフ is used more commonly for restaurant menu, such as ビーフシチュー and ビーフカレー.
If you want to express the same thing using 牛肉, you cannot simply use 牛肉シチュー - that's unnatural grammatically - but you have to say 牛肉のシチュー. Same goes for 〜カレー and other types of food involving beef.
That said, in both cases, the ビーフ prefix is more commonly used when conjugating with Katakana related to food, according to personal experience and google number of search results.
However, this is only for the case with 牛肉. When 牛 is used alone - such as in food like 牛丼 and 牛カツ - it is very common, and what I have said above may not apply.
Likewise goes for conjugation/usage with non-foodstuff - 牛肉 is more likely to be used. In this case, even for Katakana, for example 牛肉アレルギー.