Question on Video Resolution on Pioneer Plasma

I would like some to better understand video resolution.

I own a 3 years Pioneer PDP-5071HD Television. I was looking up something the other day and the manual gives the # of pixels as 1365 x 768.

I know that this is not 1080 resolutions but this is more than 720. Also the TV will state that is displaying 1080i and 1080p signals at times.

Can someone please explain this to me? Also we love the picture but would it be worth moving onto one of the newer Panasonic Plasmas?

The number of pixels is the "Native resolution" of the screen. NO MATTER WHAT the input numbers (1080p 1080i 720p), the resolution is matched to the screens native resolution.
Most flat panels made are a little taller than a true 16/9 shape (I do not know why)
Anyway, the signal is turned into what the screen will do, which for you is the native resolution of 1365x768.
The screen may be in progressive mode the 'p' or interlaced mode the 'i'
The progressive mode is more image per moment than the 'i' image. Your TV may not say it that way. The menue may say "Image for still image" or Image for best motion" instead. that is really usually the interlaced 'i' or progressive 'p'. (unfortunately for my street creed's I do NOt know which is which, offhand)
Anyway, the image is processed by your tv electronics to BE the native resolution. The 1080p image is downsized, and it's quality totally depends on the quality of the image processor inside your TV.
Also, just for info completeness. The image density for 720p is nearly identical as for 1080i. The 1080p image has TWICE the basic information, thus the image is really twice as dense as far as information delivered in 1080p.
I own a really fine 42" Plasma 720p screen, and am satisfied.
i would say for up to 50" you can live with a 720p or 1080i screen and not be too unhappy. Once the screen gets much bigger, say a 60" screen, a 1080p with a refresh rate of 120hz would be better.
The normal refresh rate is 60hz, which if you have good eyes can see the flicker. The 120 doubles the refresh rate and smooths the picture.
To decide if a bigger plasma is for you is up to you. The professional Panasonicare really great screens. i wish they made a stand alone TV tuner to match the big pannys.
Anyway i hope i helped
PS a power conditioner really does make the picture look better. Even a realitively cheap one helps.
Listen to Elizabeth. She tells the truth.

One quibble: I'm not a big fan of higher refresh rates, as they tend to present motion in a way that, to me, feels artificial.

We have 2 Panasonic plasmas, a 720 50" and a 42" 1080. Both have great pictures and I can't tell a significant difference. Possibly if I played Blue Ray on both I could but on Direct no.
Thank you for the detailed response. I am going to try an experiment in a couple of days. I have the Pioneer TV with an Oppo BDP-83 downstairs and a new Panasonic 42" G25

I am going to bring the Panasonic downstairs one day and try a side by side comparison to determine if I can see a difference.
And don't forget a good HDMI cable. Monoprice has one that is great value; I use Wireworld Silver and Van den Hul, I'm a dealer for the latter. I also replaced the power cord with a small Oyaide on both [ you have to find one with a smaller plug.] I also use power conditioners.