this years swole goals:
see my abs
deadlift 500
bench 315
artacuno53.
any time you push your body you deplete nutrients and wear yourself out. Being glycogen depleted and sore is going to make either running or lifting less effective because you won't be able to go as hard. Ultimately whichever you do second will be at less than full effort. The better option would probably be to train BWF M/W/Sa and Cardio T/R/Su to give yourself plenty of rest between the two, but real life isnt that convenient. That said: you aren't a pro bodybuilder. The 10% loss of gains or whatever isn't going to be that severe.
Taking or not taking a break between the two wont make a serious difference if you're not binging on carbs in-between. Do whatever feels best for you. The main goal should be something that you find maintainable. GJ on your weightloss, if you've made it this far the last bit will be easy