EconompicData has a nice, relatively brief post about the relationship between US Treasury bonds, TIPS, and inflation. I would hold either Treasuries or TIPS (or both) because they have the highest credit quality available, and that is a big part of why you should own bonds in the first place. Read the whole thing, but the conclusion below pretty much sums up why I prefer to have TIPS in my investment portfolio.
In normal market environments when inflation is relatively stable, long-term returns tend to be similar for both Treasuries and TIPS. However, TIPS materially outperform in an inflationary environment, while Treasury outperformance is capped by a rate roughly equal to the break-even inflation rate in a deflationary environment. Thus, assuming a view that an inflationary and deflationary scenario are equally likely, the unlimited potential outperformance of TIPS vs. Treasuries in an inflationary environment and limited upside of Treasuries vs. TIPS in a deflation environment would sway an investor towards TIPS.