I think it depends on what kind of partner you have as concerns a partnership. Concerning a proprietiorship it depends on your own business acumen. Therefore, unlimited liability can be a greater problem in either a proprietorship or a partnership.
In a partnership, your partner may rack up significant debt without you realizing it. You, however, are responsible for this debt along with your partner. It's vital you know your partner well, and their track record, if any, in business. Jumping into a partnership arrangement unsure of the business experience, motives, ethics, and more of your partner could be a recipe for disaster.
In a sole proprietorship, it's important that you know yourself! What will you be inclined to do when the going gets tough business-wise? Will you make rash decisions not based on business fundamentals that will hurt your business and cause you to incur substantial debt. If you are inclined to operating off-the-cuff then it might be better to have partner who can rein you in.
In a partnership you will supposedly share liability, as opposed to being the sole proprietor. However, you are also liable for what your partner does. In a sole proprietorship you are responsible for your actions, but only your actions. I guess you have to ask yourself if you want to be responsible for what your partner does.
I suppose it would have to be a proprietorship. Both of them have unlimited liability, but at least in a partnership you have someone else who shares the burden of the liabilities that you incur. So it's definitely a real problem in both cases, but arguably more of a problem in a sole proprietorship.