Not a disadvantage at all. I only have the Bronze DofE as well and I mentioned the DofE a lot in my application. The Gold DofE involves all the same things as Bronze does (+ an additional residential) but you just do each section for a longer period of time so you can definitely gain all the same skills from only having done Bronze.
I wouldn’t say the title of DofE is beneficial in any way for your application so mentioning “Bronze” or “Gold” will not make any difference. Instead it’s the skills that you learn from it that you should extract and use, particularly the expedition section as that involves a lot of teamwork, leadership, problem-solving, communication etc. If you talk about the DofE, you don’t have to name it, what I mean by that is you don’t have to say “as part of my Bronze DofE I worked in a team and learnt how to…” Just mentioning the word “DofE” doesn’t give you any brownie points so instead it’s far better to break down what you did for the DofE and talk about the experience by itself rather than being vague and describing as just the “DofE”.
For example, for my volunteering section of the DofE I did some fundraising to raise money to buy a defibrillator for our school, I did this in a team. Instead of saying “as part of my Bronze DofE I learnt how to work in team”, it’s better if I say “I worked in a team when fundraising to raise money for a defibrillator”.
There’s more information on how you can apply the DofE to your application here.
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