"Complex" is a difficult term. I would say that the two are both complex, but in VERY different ways.
That's why I focused on the degree to which the ingredients are transformed in the brewing process relative to winemaking. I think this is a lot of what strips the terroir out of beer.
Brewing:
- You're growing barley and possibly other cereal grains.
- You're malting that barley (allowing it to germinate and then kilning it to stop the germination process).
- Depending on how you kiln it, you can end up with very pale malt or you can end up with caramelized malt, or roasted malt. The roasted malt in a stout, for example, blows away any mild variation in flavor that you'd have in a pale malt.
- The malt is then "mashed", meaning immersed in hot water where the enzymes inherent in the malt activate and convert the starchy malt to sugar.
- The liquid (wort) is pulled out from the mash, and boiled. At this point hops are typically added.
- The hops, ESPECIALLY those added at the beginning of the boil, may be boiled for quite some time, extracting their bitterness and driving off their flavor and aroma. Only the hops added around the very end of the boil, or those added post-boil or post-fermentation (dry hopping), actually retain the flavor and aroma of the varietal.
- The wort is fermented and becomes beer.
Winemaking:
- You grow the grapes.
- You harvest the grapes, press them. They are either immediately removed from the skins (white wine) or they're left on the skins for a little bit (red wine), a couple of days IIRC.
- The grapes are naturally full of sugar (not starch) so you don't have to boil or otherwise transform them into another form before fermentation.
- You add yeast and let them ferment.
- Post-ferment, some wines are aged in oak barrels, although some may be done entirely in stainless steel.
- Tremendous complexity and winemaker interpretation can then be involved in both knowing when the wine is "ready" as well as blending various amounts of wine to achieve an intended flavor profile.
Thus in beer, the ingredients are significantly transformed at multiple steps of the process (malting, mashing, boiling), which is unnecessary for wine.
I often suggest beer vs wine is akin to baking vs cooking. Baking is very process-oriented, and cooking is more interpretive. Baking requires quality ingredients, but how much the weather affects flour from wheat grown in Iowa vs Oklahoma, for example, isn't easily evident in the final product. Cooking, in many ways, is about combining ingredients transformed as little as necessary to make them shine.
Wine is about taking the best grapes, from the places where weather/climate/soil are ideal, doing as little to transform them as possible, and letting them shine. Vintage to vintage, the "same" named wine from the same winery will taste different because the weather is different, so the grapes are different. Brewing is about combining largely standardized ingredients and pushing them through a tightly-controlled process to end up with the same result every time. Year to year, the "same" beer from the same brewery should taste identical.
