If I buy property when the market is in a downtrend the property loses
value, but I would lose money on rent anyway. So, as long I'm viewing
the property as housing expense I would be ok.
This is a bit too rough an analysis. It all depends on the numbers you plug in. Let's say you live in the Boston area, and you buy a house during a downtrend at $550k. Two years later, you need to sell it, and the best you can get is $480k. You are down $70k and you are also out two years' of property taxes, maintenance, insurance, mortgage interest maybe, etc. Say that's another $10k a year, so you are down $70k + $20k = $90k. It's probably more than that, but let's go with it...
In those same two years, you could have been living in a fairly nice apartment for $2,000/mo. In that scenario, you are out $2k * 24 months = $48k--and that's it. It's a difference of $90k - $48k = $42k in two years. That's sizable.
If I wanted to sell and upgrade to a larger property, the larger
property would also be cheaper in the downtrend.
Yes, the general rule is: if you have to spend your money on a purchase, it's best to buy when things are low, so you maximize your value.
However, if the market is in an uptrend, selling the property would
gain me more than what I paid, but larger houses would also have
increased in price.
But it may not scale. When you jump to a much larger (more expensive) house, you can think of it as buying 1.5 houses. That extra 0.5 of a house is a new purchase, and if you buy when prices are high (relative to other economic indicators, like salaries and rents), you are not doing as well as when you buy when they are low.
Do both of these scenarios negate the pro/cons of buying in either
I don't think so. I think, in general, buying "more house" (either going from an apartment to a house or from a small house to a bigger house) when housing is cheaper is favorable. Houses are goods like anything else, and when supply is high (after overproduction of them) and demand is low (during bad economic times), deals can be found relative to other times when the opposite applies, or during housing bubbles.
The other point is, as with any trend, you only know the future of the trend...after it passes. You don't know if you are buying at anything close to the bottom of a trend, though you can certainly see it is lower than it once was.
In terms of practical matters, if you are going to buy when it's up, you hope you sell when it's up, too. This graph of historical inflation-adjusted housing prices is helpful to that point: let me just say that if I bought in the latest boom, I sure hope I sold during that boom, too!