I understand that both means to emphasize the uniqueness of the word before it (i.e. "only ~") but in the following sentence, I don't know which one fits.
この難しい手術ができるのは、渡辺先生＿＿のものだ。
Both ならでは and ぐらい seem to make sense.
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～ならではの + noun is a set phrase meaning "(noun) only seen in ～", "(noun) unique to ～", "(noun) that can be done only by ～", etc. For example, you can say 渡辺先生ならではの手術, which means "surgery that can only be performed by Dr. Watanabe." (BTW, ならでは is read ならでわ)
Now, this sentence is a cleft sentence where the person name is focused. When you say "この難しい手術ができるのは", a noun (phrase) representing a person is expected after it. And 渡辺先生ならではのもの doesn't qualify as the noun phrase representing a person.
In other words, using ならでは is wrong because it would literally mean something like [×]"The person who can perform this difficult surgery is the thing that can be done only by Dr. Watanabe."
くらい/ぐらい (+ の/な + もの) is interchangeable with だけ in cleft sentences like this.
If you want to use ならでは, you can say 「この難しい手術は渡辺先生ならではのものだ」「これは渡辺先生ならではの難しい手術だ」, etc.
