Inflation Linked Bonds vs. Floating Coupon Bonds -- Which outperforms

I am wondering what would lead inflation linked bonds to outperform floating coupon bonds or vice versa.

The CFA text says that par and coupon payments are both protected from inflation under inflation linked bonds because the par amount of the bond is adjusted for inflation.

However, floating coupon bonds only have the coupon payments change and par stays flat.

Assume that we have two bonds:

Bond 1) Inflation Protected Bond - Par = $100M, I/Y= 3%

Bond 2) Floating Coupon Bond - Par = $100M, LIBOR = 2%, LIBOR Spread = 100 bps

Let’s say that in the first year, inflation was 5% when it was expected to be 3%.

Payments would be:

Bond 1) 100,000,000 * 1.05 * 3% = 3,150,000

Bond 2) LIBOR increases by 2% to account for the 2% of unanticipated inflation. = 100,000,000 * (2% + 2% + 1%) = 5,000,000

So my question is, although bond 1 has the par value protected from inflation due to its adjustment, bond 2 receives a much larger payment increase from the inflation. Due to the different payouts, I am wondering when an investor would prefer to own bond 1 vs. bond 2, and vice versa?